Imbeddings of free actions on handlebodies

Fix a free, orientation-preserving action of a finite group on a -dimensional handlebody . Whenever acts freely preserving orientation on a connected -manifold , there is a -equivariant imbedding of into . There are choices of closed and Seifert-fibered for which the image of is a handlebody of a Heegaard splitting of . Provided that the genus of is at least , there are similar choices with closed and hyperbolic.

     

Bergman-Type Reproducing Kernels, Contractive Divisors, and Dilations

Let Ω be a region in the complex plane. In this paper we introduce a class of sesquianalytic reproducing kernels on Ω that we call B-kernels. When Ω is the open unit disk and certain natural additional hypotheses are added we call such kernels k Bergman-type kernels. In this case the associated reproducing kernel Hilbert space (k) shares certain properties with the classical Bergman space L²_α of the unit disk. For example, the weighted Bergman kernels k^β_w(z)=(1−wz)^−β, 1β2 are Bergman-type kernels. Furthermore, for any Bergman-type kernel k one has H² (k)L²_a, where the inclusion maps are contractive, and M_ζ, the operator of multiplication with the identity function ζ, defines a contraction operator on (k). Our main results about Bergman-type kernels k are the following two: First, once properly normalized, the reproducing kernel for any nontrivial zero based invariant subspace of (k) is a Bergman-type kernel as well. For the weighted Bergman kernels k^β this result even holds for all _ζ-invariant subspace of index 1, i.e., whenever the dimension of /ζ is one. Second, if is any multiplier invariant subspace of (k), and if we set *= z , then M_ζ is unitarily equivalent to M_ζ acting on a space of *-valued analytic functions with an operator-valued reproducing kernel of the type

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where V is a contractive analytic function V :  → ( ,  *), for some auxiliary Hilbert space . Parts of these theorems hold in more generality. Corollaries include contractive divisor, wandering subspace, and dilation theorems for all Bergman-type reproducing kernel Hilbert spaces. When restricted to index one invariant subspaces of (k^β), 1β2, our approach yields new proofs of the contractive divisor property, the strong contractive divisor property, and the wandering subspace theorems and inner–outer factorization. Our proofs are based on the properties of reproducing kernels, and they do not involve the use of biharmonic Green functions as had some of the earlier proofs.     

Simple Zeros of the Riemann Zeta-Function

Assuming the Riemann Hypothesis, Montgomery showed by meansof his pair correlation method that at least two-thirds of thezeros of Riemann's zeta-function are simple. Later he and Taylorimproved this to 67.25 percent and, more recently, Cheer andGoldston increased the percentage to 67.2753. Here we proveby a new method that if the Riemann and Generalized LindelöofHypotheses hold, then at least 70.3704 percent of the zerosare simple and at least 84.5679 percent are distinct. Our methoduses mean value estimates for various functions defined by Dirichletseries sampled at the zeros of the Riemann zeta-function. 1991Mathematics Subject Classification: 11M26.     

N2-time-dependent SCF scheme

A new procedure for the Fock matrix operator construction is proposed. Its application for RHF calculations on diatomic molecules using Slater orbital basis sets shows that the computation time for the new SCF procedure is proportional to the square of the basis set size.     

Transformation of solvent-derived ozonolysis products to bicyclic peroxides: Isolation and characterisation of novel pentoxonane derivatives

-Hydroperoxyisochroman derivatives 5 react with formaldehyde under acidic conditions to produce mixtures of bicyclic 1,2,4,6-tetroxepane 9 and 1,2,4,6,8-pentoxonane 10 derivatives. The structure of the compound 10a was unambiguously established by the X-ray analysis. With acetaldehyde, only the corresponding 1,2,4,6-tetroxepanes 9 were obtained.     

The trisecant identity and operator theory

For the special case of a Riemann surface which arises as the double of a planar domainR, the trisecant identity has a natural interpretation as a relation among reproducing kernels for subspaces of the Hardy spaceH ² (R). This relation and Riemann's theorem on the vanishing of the theta function is applied to Nevanlinna-Pick interpolation onR.     

Melting-point purity determinations: Limitations as evidenced by calorimetric studies in the melting region

Typical melting curves, chosen from the results of more than 125 melting-point studies, are presented to illustrate both the reliability and the inherent limitations of the calorimetric method of purity determination. It is shown that this method usually is one of the best means of accurately determining small concentrations of impurity. However, analysis of anomalous melting curves leads to the conclusion that pseudo-equilibrium curves are often obtained as a result of inhomogeneous distribution of impurity in the liquid phase or of non-equilibrium distribution of impurity between the solid and liquid phases. Evidence is given to support the contention that solidsolutions were formed in as many as half of the samples studied and that for this reason, impurity values calculated for perhaps $\text{1}\text{3}$ of the samples are in error by 200% or more. Although these large uncertainties in impurity values usually correspond to less than 0.1 % uncertainty in purity values, modified procedures are proposed to minimize such errors.